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Phase transitions in shape memory alloys: a non-isothermal Ginzburg-Landau model. (English) Zbl 1189.82081
Summary: We propose a model to describe non-isothermal transitions from the austenite to the martensite phase occurring in shape memory materials. The phenomenon is set in the context of the Ginzburg-Landau theory of phase transitions, postulating a free energy depending on the temperature, the stress and the order parameter. In the one-dimensional case, when only two martensitic variants are involved and stress and deformation have a fixed direction, our choice of free energy allows us to deduce a phase diagram describing the main features of a typical SMA. The Ginzburg-Landau equation ruling the evolution of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive equation relating stress, strain and order parameter. The consistency of the model with the second law of Thermodynamics in the form of the Clausius-Duhem inequality is proved. Finally a possible generalization to a three-dimensional model is proposed, by introducing a tensor-valued order parameter.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q56 Ginzburg-Landau equations
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